Question

Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p-value.

Short answer

The graph shown below is based on the situation given.

Step-by-step solution

Given Information

• The Whites born in $1900$had a life expectancy of $47.6$ years
• The nonwhites had a life expectancy of $33.0$ years.
• The average life duration of the 124 whites was 45.3 years, with a standard deviation of 12.7 years.
• The average life span of the 82 nonwhites was 34.1 years, with a standard deviation of 15.6 years.

Marking the hypothesized difference and the sample difference and Shade the area corresponding to the p-value. 

The p-value in the graph is